For the next steps, the plan is to build a 4-port Butler matrix in hardware and measure it’s S-parameters and then grow this design to a full 16-port Butler matrix to operate over wider bandwidths.
In order to characterize each of the 180o surface mount hybrids purchased from Werlatone, it was necessary to develop a test fixture comprised of two parts. The first is the mechanical holder used to hold and align the hybrid part during the testing. The second is the circuit board that will provide the RF connection to the hybrid. The mechanical holder also includes an RF path from the circuit board to the hybrid. Figure 27 shows the overview of the holder assembly.
Figure 27: Test fixture to characterize the 180deg surface mounts
The device under test (DUT) is the Werlatone model H10126 180o hybrid whose performance is shown in Figure 10. The DUT is approximately 0.1” X 0.6” X 0.1” and uses the four ports as shown in Figure 9.
These four ports are located at the corners of the device. To enable the test fixture to measure the DUT in a non-destructive manner, the fixture utilizes a pogo pin shown in Figure 28. A pogo pin, also known as a spring-loaded pin, is a type of electrical connector mechanism that is often used for testing purposes. In this test fixture, the pogo pin provides an RF path to the DUT without requiring it to be soldered to the device.
The top section of the pin compresses into the body while still maintaining RF connectivity across the pin.
The length of the pin is approximately 0.14 inches in length and 0.04 inches in diameter and it is attached to the circuit board as shown in Figure 29
Figure 28: Pogo pin
(a) (b)
Figure 29: (a) Top side of circuit board and (b) bottom side of circuit board
In order to maintain the 50Ω impedance that is provided by the microstrip line up to the hybrid connection point, the pogo pin acts like the center conductor of a coaxial cable. Additionally, the diameters of the feed-thru holes are designed based on the formula for a standard coaxial structure as shown in Eq.
(18). Knowing the center conductor diameter, 𝐷𝑐𝑒𝑛𝑡𝑒𝑟, the outer diameter of the coaxial can be calculated from the formula for a 50 Ω impedance.
𝐷𝑜𝑢𝑡𝑒𝑟 = 𝐷𝑐𝑒𝑛𝑡𝑒𝑟× 10(0.362 ×√𝑒𝑟) (18)
In Eq. (18) the parameter, 𝑒𝑟, is the dielectric constant of the material between the center and outer conductors. A cross-section of the pin and plate is shown in Figure 30. Table 4 gives the details of design.
(a) (b)
Figure 30: (a) Pogo pin outline with the 4 sections and (b) Feed-thru outline in the fixture RF Inputs
RF Outputs
Pogo pins
Pogo pins
Section 4 Section 3
Section 2 Section 1
Table 4: Inner and outer diameters for the coaxial cable feed-thrus
Since part of the pin is located in the circuit board, the outer wall of the coaxial structure is made by a series of vias placed on a circular pattern as shown in Figure 31. This is done to maintain the 50 impedance.
Figure 31: Top layer of the circuit board
To verify the performance of the circuit board and pogo pin interface, an electromagnetic (EM) model of the assembly was generated in FEKO [12]. FEKO is a Method of Moments code that is used to model antenna and circuit structures. Figure 32 shows the layout of a single trace associated with the test assembly.
The Voltage Standing Wave Ratio (VSWR) of the test assembly is shown in Figure 33 and the input impedance represented on a Smith chart is displayed in Figure 34. The results show that there is some reactance associated with this structure and will need to be further investigated to understand the causes of this reactance and how to mitigate it.
Hybrid
Coaxial Vias
Figure 32: Single trace microstrip to pogo feed-thru
Figure 33: VSWR of input port trace (50 ohm terminated)
Figure 34: Smith chart representation of the input impedance
5.1 4 X 4 Beamformer Design
Once these hybrids are fully characterized, the data will be used to start the design of the 4 × 4 beamforming network. In order to remove the cross-over needed, as shown in Figure 35, the hybrids are placed on a circular arc, shown in Figure 35a, which removes the need for cross-overs but now places some of the input and output ports in the center of the circle, where they will be hard to access. Since the design of a hybrid is such that each port can be accessed from either side, the hybrids can be configured such that the ports that are on the inside of the circle can be placed on the outside by simply flipping the hybrids.
Figure 35b shows that by flipping hybrids 3 and 4 all of the hybrid ports now reside on the outside of the circle and we have also managed to get rid of the need for any cross-overs.
When designing the 90o phase shift circuit, stripline techniques can help improve the bandwidth performance of this structure over conventional microstrip techniques due to the wideband characteristics of the even- and odd-impedances associated with coupled lines. A conceptual design for the full 4 × 4 beamformer is shown in Figure 36a. In this layout all the reference and phase shift lines will be constructed using stripline techniques, as shown in Figure 36b, while the input and output from the beamformer will use microstrip lines. When constructing the final 16 × 16 port beamformer the new construction techniques will be used where possible. Details of the design will be discussed in a future report.
(a) Original Layout (b) Flipped Design
Figure 35: 4 × 4 Beamformer layout configurations
(a) Top layer using microstrip design (b) Middle layer using stripline design
Figure 36: 4 × 4 beamformer assembly